1. Field of the Invention
The present invention relates to an electromagnetic field simulator and an electromagnetic field simulation program for conducting electromagnetic field simulation. More particularly, the present invention relates to an electromagnetic field simulator which enables the reduction of computation cost and decrease in computation error when the simulation is conducted by a FDTD method.
2. Description of the Related Art
A finite difference time domain (FDTD) method has been known as a method for electromagnetic field simulation (for example, see Yee, K. S., “Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media”, IEEE Transa. Antennas Propagat., Vol.Ap-14, p. 302-307, 1966; Uno Toru, “Analysis of electromagnetic field and antenna by FDTD method”, 1998, Corona Co.).
With the FDTD method, the Maxwell's equation, which is basic equation describing the change of electromagnetic field with time, is differentiated with respect to space and time to trace the changes in the electromagnetic field with time. In this case, a detailed simulation of change in electromagnetic field with time can be performed by setting a sufficiently small grid spacing (step) used for space and time discretization.
The FDTD method has the following advantages. Because the Maxwell's equation is computed directly, three-dimensional computation is simple; because the calculation of electromagnetic field in each grid is conducted by referring only to the electromagnetic field in the spatially adjacent grid, the computation principle is simple and the calculation speed is high and, therefore, parallel processing in which a analytical model is divided and computed at the same time in different computers is simple; and a time waveform in principle can be computed.
On the other hand, a technology for accessing information storage media with light has recently been developed, a near-field optics using optical element with a structure smaller than the light wavelength has attracted attention, and the analysis of light behavior in microscopic regions that are several times the light wavelength was often conducted.
In such near-field optics, the light cannot be handled as a light ray. Therefore, the light can be effectively analyzed as an electromagnetic wave with the electromagnetic field simulator using the FDTD method. A research of the near-field optics by employing such FDTD method in the optical model has been abundantly conducted.
However, if the FDTD method is used for optical analysis such as the behavior of light that irradiates a substance, problems are associated with the material constants (permittivity and electric conductivity) of the substance, by contrast with the general electromagnetic wave analysis focused on microwave, radio wave and so on.
Thus, the permittivity of the metal often has a negative value, and the problem arising when they are directly employed in the FDTD method is that the value diverges exponentially with the advancement of time steps in the computational formula.
In order to resolve this problem, the computation is conducted, for example, by handing an electric current inside a substance that is generated due to the absorption of the electromagnetic wave as a polarization current induced inside the substance (for example, Justin B. Judkins and Richard W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film gratings”, J. Opt. Soc. Am. A Vol.12, No.9, p. 1974-1983, 1995).
However, a computational error sometimes occurs between the computations conducted by the FDTD method based on the polarization current, which is described in the reference above, and the rigorous computation.
For example, when a transmittance is computed by the FDTD method using the polarization current and when rigorous computations are conducted in the case of simulating a model in which a thin metal film is irradiated with light, the computational error increases with the increase in the grid spacing.
In order to reduce this error, the grid spacing may be sufficiently decreased, but the resultant problems are that the computation speed deceases accordingly, a large memory capacity is necessary for the computation, and the computation cost rises. On the other hand, if the grid spacing is increased, the error increases and reliability of the computation results drops, thereby making it difficult to consider the results as approximate.
In order to employ the simulation using the FDTD method for design, it is necessary to obtain the computation results that can be considered as approximate value even in the case of coarse computations with a sufficiently large grid spacing, and there is a strong demand for such computation procedure. This is because increasing the grid spacing of the analytical model in the process of obtaining approximate result and shortening the computation time leads to a significant reduction in the number of design steps.